In [1]}, the stability scattering diagram for \(\mathcal {C}=D^b\operatorname{Coh}_c({P}^2)\) 
was constructed for the one-parameter family of stability conditions of the form (REF ),
assuming the special value \(\psi =0\)  for the phase. The construction was performed
using a different set of coordinates \((x,y)=(s,\frac{1}{2}(t^2-s^2))\)  with \(y>-\frac{1}{2} x^2\) , such that the rays \(\mathcal {R}_0(\gamma )\) 
become segments of
straight lines \(ry+dx-\textnormal {ch}_2=0\) , similar to standard
affine scattering diagrams
in the context of mirror symmetry [2]}, [3]}.
The main result of this analysis is that the initial rays of the resulting diagram,
which we denote by
\(\mathcal {D}^{\rm LV}_0\) ,
consist of a pair of rays \(\mathcal {R}_0(\mathcal {O}(m))\)  and \(\mathcal {R}_0(\mathcal {O}(m)[1])\) 
emitted from every integer points \((x,y)=(m,-\frac{1}{2} m^2)\in {Z}\)  tangent to the parabola \(y=-\frac{1}{2} x^2\) ,
where the central charge of the coherent sheaf \(\mathcal {O}(m)\)  vanishesIndeed,
\(Z^{\rm LV}_{(s,t)}(\gamma )=-\frac{1}{2}(s+It-m)^2\)  for \(\gamma =[1,m,\frac{1}{2} m^2]\) .,
see Figure REF .
